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High School Physics Practice Test

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A 0.5 kg ball collides inelastically with a 0.5 kg ball at rest; after the collision they move together with velocity v. If the first ball's initial velocity is u, what is the final velocity?
Correct Answer:
v_final = 0.5u.
Explanation:
In collisions with no external forces, momentum is conserved. If the two 0.5 kg balls stick together, the total mass after the collision is 1.0 kg. The initial momentum comes only from the moving ball: p_i = (0.5 kg) × u = 0.5u. After sticking, they move as a single 1.0 kg object, so (1.0 kg) × v = 0.5u, giving v = 0.5u. So the final velocity is half of the initial velocity. (Kinetic energy isn’t conserved in inelastic collisions—the momentum is, but some energy is lost to deformation, heat, etc.)

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